Modeling Excess Life in Cellular Telecommunications Networks

1
Modeling Excess Life in Cellular
Telecommunications Networks
Advisors Yi-Bing Lin Hui-Nien
Hung???????????
Student Pei-Chun Lee?????

• Main research issue
• Random number (RN) generation for excess life of
  MS cell residence time
• Application examples
• Dynamic periodic location area update
• Modeling channel assignment of small-scale
  cellular networks

• Application of Theorem 1 (applied
• in simulation)
• Generate an RN a for the uniform random variable
  U in (0,1)
• Generate an RN b for the random variable T with
  the density function fT (t )(Note U and T are
  obviously independent.)
• Set the excess life to a?b

Theorem 1 If U is uniformly distributed over the
interval (0,1), T has the density function fT (t
) t fm(t ) /m, where fm(t ) and m are the
density function and the mean of the MS cell
residence time, and U and T are independent,
then the excess life of the MS cell residence
time has the same distribution as that of U?T.
Note T distribution needs to be derived
according to the MS cell residence time
distribution.
Example Theorem 2 If the MS cell residence
time has a gamma distribution with parameters (a,
b ), then T has a gamma distribution
with parameters (a 1, b ).

• Figure The excess life density function, rm(tm
  ), for gamma MS cell residence time, where
• tm excess life of the MS cell residence time
• m mean of the MS cell residence time
• var variance of the MS cell residence time